Inversion of channel distortion by adaptive wavelet lifting

ABSTRACT

A method for inverting telecommunication channel distortion by adaptive wavelet lifting. The distortion signal is analyzed using wavelet lifting and the inverse filter is computed. Coefficients of the inverse filter are used to either compute a transmission pre-filter or to update the transmitted message.

BACKGROUND

1. Field of the Invention

The invention relates to methods for encoding and transmitting data orinformation; more specifically the invention is a method for invertingdistortion processes in a telecommunication channel.

2. Current Art and Problem Solution Needed

Recent information technology advancements such as real-time multimediaapplications and high-speed Internet access, as well as the integrationof common communications means such as telephone, Internet, television,and digital data systems have led to an unprecedented need forhigh-speed data transfer. However, many segments of today's wirednetworks are incapable of supporting the transfer rates required bythese technologies. In many cases, it is impractical, both physicallyand economically, to install the necessary fiber optic and otherbroadband infrastructures to overcome this deficiency. Furthermore, incertain circumstances such as emergencies and military operationsrequiring high-speed data transfer, there exists an inherent need forrapid and temporary network access deployment, precluding fiber andtraditional wireless systems, which have rather long lead-times.

An examination of existing legacy landline communications networks inlight of communications technology evolution leads to some interestingobservations. On the one hand, the newest long haul communications andinformation infrastructures being built today are based on fiber opticand coding technologies that are capable of immense capacity. On theother hand, the “last mile” local drop to the end user is typicallystill the legacy copper line installed decades ago for telephoneservice. Because the legacy copper lines were designed for performancethat did not contemplate today's fiber optic capabilities, presentcopper line technologies cannot avail end users of the high bit ratesthat modern long haul infrastructure can provide. The user is limited byhis local drop connection to the service provider.

Looking at the communications system architectures currently beingpursued by service providers, nearly all suffer from implicitassumptions that preserve the notion of connection-based service.

The use of telecommunication resources has moved well beyond meretelephone calls. These voice communications messages are no longer thedominant kind of information flowing through the world's communicationnetworks. Telecommunication users today utilize these resources for manyother forms of information. Computer data and video are just examples ofthe future. Users are requiring that their communication link to theglobal networks rise to the occasion in terms of bandwidth, that is,digital data rate capability. The legacy links as well as thearchitecture of the central office (telephone exchange) and its cable tothe user cannot deliver the information capability desired for all thisdata, video and other information. However, a somewhat recentdevelopment is the application of digital technology to legacy coppersystems—a development variously designated as “xDSL.”

xDSL is a generic term for digital subscriber line equipment andservices, including packet-based architectures, such as ADSL, HDSL,SDSL, VDSL, and RADSL. That is, x is the generic. xDSL technologiesprovide extremely high bandwidth over embedded twisted pair, coppercable plant. xDSL technologies offer great potential forbandwidth-intensive applications, such as Internet access, remote LANaccess, video conferencing, and video-on-demand.

ADSL or asymmetric digital subscriber line services generally useexisting unshielded twisted pair (UTP) copper wires from the telephonecompany's central office to the subscriber's premise, utilize electronicequipment in the form of ADSL modems at both the central office and thesubscriber's premise, send high-speed digital signals up and down thosecopper wires, and send more information one way than the other. The ADSLflavor of xDSL services is capable of providing a downstream bandwidthof about 1.5 Mbps-6.144 Mbps, and an upstream bandwidth of about 32Kbps-640 Kbps with loop distances ranging from about 3.7 km-5.5 km. HDSLor high bit rate digital subscriber line services provide a symmetric,high-performance connection over a shorter loop, and typically requiretwo or three copper twisted pairs. HDSL is capable of providing bothupstream and downstream bandwidth of about 1.5 Mbps, over loop distancesof up to about 3.7 km. SDSL or single line digital subscriber lineservices provide a symmetric connection that matches HDSL performanceusing a single twisted pair, but operating over a shorter loop of up toabout 3.0 km. VDSL or very high bit rate digital subscriber lineservices are typically implemented in asymmetric form, as a very highspeed variation on the ADSL theme over a very short loop. Specifically,target downstream performance is typically about 52 Mbps over UTP localloops of 300 m, 26 Mbps at 1,000 m, and 13 Mbps at 1,500 m. Upstreamdata rates in asymmetric implementations tend to range from about 1.6Mbps to about 2.3 Mbps. Additionally, there is RADSL or rate adaptivedigital subscriber line services. RADSL provides a dynamic connectionthat adapts to the length and quality of the line.

In the xDSL family of services, many xDSL themes, including ADSL, HDSL,SDSL, VDSL, and RADSL, utilize a packet-based approach that does awaywith the line-grabbing practice of circuit switched networks, such asISDN (although ISDN service is a form of digital subscriber line). Thispacket-based approach is very advantageous in a variety of situations,such as high-speed data services, including high definition televisionor HDTV transmissions.

xDSL services, also commonly referred to as simply DSL or digitalsubscriber line services, are much more dependent on line conditionsthan traditional telephone services. Traditional telephone servicestypically use a bandwidth including frequencies up to about 3 kilohertz,while the DSL services utilize a bandwidth including frequencies up intothe hundreds of kilohertz. While some local loops are in great conditionfor implementing DSL services, that is, the local loops have short tomoderate lengths with minimal bridged taps and splices, many local loopsare not as clean. For example, local loop length vary widely, forexample, from as short as a few hundred meters to as long as severalkilometers

SUMMARY

In response to the need for improved telecommunications systems thatwill transmit faster and more reliably, herein is disclosed a system andmethod for inverting noise and distortion encountered in thetelecommunications channel and transmission equipment.

The system and method is disclosed comprising a transmitter and receiverusing wavelets for constructing signals that, when transmitted by thetransmitter, said signals are received by the receiver and are maximallydiscriminable by the receiver.

The system and method is disclosed comprising filter-banks for wavelets,whereby the filter-banks use the method of lifting to construct signalsthat are maximally discriminable by the receiver.

A first aspect of the system and method is disclosed comprising anapparatus that implements the following process: (1) with a message, thetransmitter using a first filter bank and wavelet lifting, constructs asignal from the message, and sends the signal to the receiver, whereinthe signal sent by the transmitter is known to the receiver; (2) thereceiver receives the signal and compares the signal to an expectedsignal, to form a novelty signal, wherein the expected signal is thesignal known to the receiver, and has been distorted by the channel in amanner that is expected by the receiver; if the novelty signal issufficiently small, the receiver notifies the transmitter and thetransmitter and receiver utilize the first signal to communicate; if thenovelty signal is greater than a predetermined signal, the apparatusprocesses signals according to the following: (3) the receiver, using asecond wavelet filter bank (an analysis filter bank) that is known tothe transmitter, computes the coefficients that are required torepresent the novelty signal in terms of the second filter bank; thereceiver computes the coefficients of the synthesis filter bank that isrelated to the second filter bank, whereby the synthesis filter bank isthe inverse filter bank to the second filter bank; (4) the receiversends the coefficients of the inverse filter bank to the transmitter;(5) the transmitter computes an updated first filter bank using theprevious first filter bank and the coefficients of the inverse of thesecond filter bank; (6) the transmitter, using the updated filter bankand the process of lifting, constructs an updated signal and sends theupdated signal to the receiver; (7) the updated signal is processedaccording to (2), above.

A second aspect of the system and method is disclosed comprising anapparatus that implements the following process: (1) with a message, thetransmitter using a first filter bank and wavelet lifting, constructs asignal, and sends the signal to the receiver, wherein the signal sent bythe transmitter is known to the receiver; (2) the receiver receives thesignal and compares the signal to an expected signal, to form a noveltysignal, wherein the expected signal is the signal known to the receiver,and has been distorted by the channel in a manner that is expected bythe receiver; if the novelty signal is sufficiently small, the receivernotifies the transmitter and the transmitter and receiver utilize thefirst signal to communicate; if the novelty signal is greater than apredetermined signal, the apparatus processes signals according to thefollowing: (3) the receiver, using a second wavelet filter bank (ananalysis filter bank) that is known to the transmitter, computes thecoefficients that are required to represent the novelty signal in termsof the second filter bank; the receiver computes the coefficients of thesynthesis filter bank that is related to the second filter bank, wherebythe synthesis filter bank is the inverse filter bank to the secondfilter bank; (4) the receiver sends the coefficients of the inversefilter bank to the transmitter; (5) the transmitter computes an updatedmessage using the previous first filter bank and the coefficients of theinverse of the second filter bank; (6) the transmitter, using theupdated message, the first filter bank and the process of lifting,constructs an updated signal and sends the updated signal to thereceiver; (7) the updated signal is processed according to (2), above.

A variant of either the first aspect or the second aspect of the systemand method described above is for all filter bank processing to beperformed in the transmitter, whereby the receiver computes andtransmits the novelty signal to the transmitter.

Another variant of either the first aspect or the second aspect of thesystem and method described above is for the receiver to select a filterbank that is amenable to analyzing the novelty signal, and sending theidentity of the analysis filter bank with the coefficients of theinverse filter bank.

Another variant of either the first aspect of the second aspect of thesystem and method described above is for the first filter bank and thesecond filter bank to be identical.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a single stage of a filter bank.

FIG. 2 is a diagram showing possible computing devices for implementingaspects of the system and method disclosed herein.

FIG. 3 comprises Matlab code for implementing a filter bank for the Haarwavelet using the lifting method.

FIG. 4 comprises Matlab code for implementing a filter bank for theDaubechies D4 transform using the lifting method. Matlab code for bothforward and inverse lifting are shown.

FIG. 5 is flow chart of a first aspect of the invention.

FIG. 6 is a flow chart of a second aspect of the invention.

DETAILED DESCRIPTION

Wavelets and Filter Banks

With respect to FIG. 1, a filter-bank is a mathematical representationand model of actual physical filters used in signal processing; filterbanks model filters responding to and interacting with certain aspectsof a signal.

Certain kinds of filter banks, such as “quadrature mirror filters” havedesirable properties for representing signal processing, wherein signalsrepresented by these filter banks can be compressed and perfectlyreconstructed. These filters are also associated with certain functionscalled wavelets, which are derived from filters using the “cascadealgorithm”.

A complete discussion of filter banks, wavelets and the mathematicalrequirements for distortion and alias-free signal construction can befound in Wavelets and Filter Banks by Strang and Nguyen.

Computational Environment

FIG. 2 illustrates a generalized example of a suitable computingenvironment 200 in which the disclosed embodiments may be implemented.The computing environment 200 is not intended to suggest any limitationas to scope of use or functionality of the invention, as the presentinvention may be implemented in diverse general-purpose orspecial-purpose computing environments.

With reference to FIG. 2, the computing environment 200 includes atleast one processing unit 210 and memory 220. In FIG. 2, this most basicconfiguration 230 is included within a dashed line. The processing unit210 executes computer-executable instructions and may be a real or avirtual processor. In a multi-processing system, multiple processingunits execute computer-executable instructions to increase processingpower. The memory 220 may be volatile memory (e.g., registers, cache,RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory, etc.), orsome combination of the two. The memory 220 stores software 280implementing wavelet lifting and associated algorithms required toimplement and practice the invention.

A computing environment for other aspects of the invention may haveadditional features. For example, the computing environment 200 includesstorage 240, one or more input devices 250, one or more output devices260, and one or more communication connections 270. An interconnectionmechanism (not shown) such as a bus, controller, or networkinterconnects the components of the computing environment 200.Typically, operating system software (not shown) provides an operatingenvironment for other software executing in the computing environment200, and coordinates activities of the components of the computingenvironment 200.

The storage 240 may be removable or non-removable, and includes magneticdisks, magnetic tapes or cassettes, CD-ROMs, DVDs, or any other mediumwhich can be used to store information and which can be accessed withinthe computing environment 200. The storage 240 stores instructions forsoftware 280 and data.

The input device(s) 250 may be a touch input device such as a keyboard,mouse, pen, or trackball, a voice input device, a scanning device, oranother device that provides input to the computing environment 200. Foraudio or video, the input device(s) 250 may be a sound card, video card,TV tuner card, or similar device that accepts audio or video input inanalog or digital form. The output device(s) 260 may be a display,printer, speaker, or another device that provides output from thecomputing environment 200.

The communication connection(s) 270 enable the carrier which ismodulated by the transmitter and demodulated by the receiver. Thecommunication medium conveys information such as computer-executableinstructions, compressed audio or video information, or other data in amodulated data signal. A modulated data signal is a signal that has oneor more of its characteristics set or changed in such a manner as toencode information in the signal. By way of example, and not limitation,communication media include wired or wireless techniques implementedwith an electrical, optical, RF, infrared, acoustic, or other carrier.

The invention can be described in the general context ofcomputer-readable media. Computer-readable media are any available mediathat can be accessed within a computing environment. By way of example,and not limitation, with the computing environment 200,computer-readable media include memory 220, storage 240, communicationmedia, and combinations of any of the above.

The invention can be described in the general context ofcomputer-executable instructions, such as those included in programmodules, being executed in a computing environment on a target real orvirtual processor. In the disclosed aspects of the invention, programmodules are executed for (1) controlling a transmitter and controlling areceiver; (2) modulating a carrier by the transmitter using a signal;(3) analyzing and characterizing the transmission process to determinethe relationship of signal distortion to signal structure and content,including computing operators by wavelet lifting to analyze and toinvert the effects of signal distortion; (4) constructing and selectinga set of signals, wherein selection and construction is made accordingto the relationship of signal distortion to signal structure andcontent, and; (5) encoding a message or part of a message using one ofthe digital signals selected from the set of digital signals, anddecoding a digital signal to derive a message or part of a message.

Generally, program modules include routines, programs, libraries,objects, classes, components, data structures, etc. that performparticular tasks or implement particular abstract data types. Thefunctionality of the program modules may be combined or split betweenprogram modules as desired operations performed by a computer, andshould not be confused with acts performed by a human being. The actualcomputer operations corresponding to these terms vary depending onimplementation.

The program modules are written in a programming language selected forthe particular computer used in the apparatus; the language selectedfrom C, C++, Visual BASIC, Java, assembly language, Fortran and soforth.

It will be appreciated that functions or processes that are described interms of software can be implemented in hardware devices such as ASICs(application specific integrated circuits), FPGA (field programmablegate arrays) or the like. Similarly, functions or processes that aredescribed as hardware devices can also be implemented in software.

Wavelet Construction by “Lifting”

See either of the following references for a complete discussion ofwavelet lifting. (1). I. Daubechies and Wim Sweldens, Factoring WaveletTransforms into Lifting Steps, Journal of Fourier Analysis andApplications, Volume 4, Number 3, 1998. (2). C. Valens, The Fast LiftingWavelet Transform, c.valens@mindless.com)

The one-dimensional discrete wavelet transform DWT represents areal-valued discrete-time signal in terms of shifts and dilations of alow-pass filter or scaling function and a band-pass wavelet function.The DWT decomposition of a signal is multi-scale: at stage j the DWTdecomposes a signal into a set of scaling coefficients c^(j)(n), where nis the sample number of the signal, and represents coarse signalinformation or coarse detail at the scale level j; and the set ofwavelet coefficients, d^(j)(n), which represents “fine” detail of thesignal at the scale j; the signal is recursively decomposed into the twosets of coefficients for scales j=1, 2, 3 . . . N.

The inverse DWT employs inverse filters to reconstruct the signal fromthe sets of coefficients.

A DWT can be implemented as a predictor-corrector decomposition, inwhich the scaling coefficients at scale level j are used as predictorsfor the signal at the next higher or finer level of detail at scale j+1.Wavelet coefficients are the prediction errors between the scalingcoefficients and the higher-level signal details the scalingcoefficients predict. This interpretation of the DWT leads to theconcept of wavelet decomposition by lifting.

The term “lifting” applies to the process of starting with an elementarywavelet and mathematically “lifting the wavelet” to higher complexity,wherein the additional complexity gives the lifted wavelet certaindesired properties.

With respect to FIG. 1, the diagram depicts a single stage of the DWT bylifting. Lifting is a spatial or time-domain process for constructingbi-orthogonal wavelets. In the lifting form of the DWT samples of asignal x(n) are decomposed into two sets, and predictor-corrector orupdate operators, P and U are applied between the two sets of signalvalues to derive the DWT decomposition.

Lifting Method

With respect to FIGS. 3, 4 and 5, the lifting method comprises:

-   1. Divide input x(n) into two disjoint sets, in this example x(n) is    divided into an “even” set, where n is an even number and an “odd”    set, where n is an odd number.-   2. Update x_(E)(n) and d(n) and compute scaling coefficients to    represent a coarse approximation to the original signal x(n);    U(d(n)) is the update operator and is usually chosen to be zero when    the algorithm is initialized:    c(n)=x _(E)(n)+U(d(n)).  EQN. LA-1-   3. Compute wavelet coefficients d(n) as the error in predicting    x_(O)(n) from x_(E)(n) using the prediction operator, P:    d(n)=x _(O)(n)−P(x _(E)(n))  EQN. LA-2    Inversion—Generating the Original Signal from the Lifting    Coefficients

The original signal is computed from the lifting coefficients by:x _(E)(n)=c(n)−U(d(n))  EQN. LA-3x _(O)(n)=d(n)+P(x _(E)(n))  EQN. LA-4Redundant Lifting

In redundant lifting, an additional prediction is added through thefollowing equation:e(n)=x _(E)(n)−Q(x _(O)(n))  EQN. LA-5In this equation, the even coefficients are predicted from the oddcoefficients. The update equation EQN LA-1 is modified as:c(n)=x _(E)(n)+V(d(n),e(n)).  EQN. LA-6Lifting and De-Noising Wavelets

Because wavelet coefficients comprise a compact representation ofsignals at varying levels of detail, processing of these coefficientsprovide a simple means of removing noise from a signal. Assume a signals(n) is corrupted by noise ξ(n), where s and ξ are sampled at discreteinstances of time n and ξ is an additive Gaussian source. Samples x(n)of the unknown signal are observed; where:x(n)=s(n)+ξ(n)

The discrete wavelet transform (DWT) of x(n) is computed, and anon-linear threshold, proportional to the standard deviation of thenoise, is applied to all coefficients. All coefficients below thethreshold are set to zero, for “hard thresholding”. For softthresholding all coefficients below the threshold are set to zero, andall other coefficients are reduced by the threshold amount. Thethreshold is selected so the thresholding operation leaves the scalingcoefficients largely unaffected. If s(n)=0 for all n sampled, and ξ ispure Gaussian white noise, it can be shown that as the number of sampledpoints increase, the wavelet thresholding estimator function tends tothe zero function with probability one (this basically means that thelifting process can “lock onto” the noise signal; see D. L. Donoho,Denoising by soft-thresholding, IEEE Transactions on Information Theory,volume 41, pp. 613-627, 1995). Therefore with the proper adaptivelifting algorithms, noise can be effectively removed from the signal.

Finding Optimal Waveforms by Adaptive Lifting—a First Aspect of theInvention

Lifting will be used to construct a set of base signals that are bestsuited for a given transmission system. By best suited, it is meant aset of base signals that are maximally discriminable by a receiver inthe transmission system. Base signals are constructed in real-time by anadaptive lifting algorithm.

With respect to FIG. 5 the adaptive lifting method for optimal basesignal construction comprises:

-   -   1. A wavelet, ω, is selected and a message, σ is used to encode        the wavelet to form a base-band signal σ_(ω).    -   2. The base-band signal is either sent over a transmission        system T or is used to modulate a carrier ζ associated with T.    -   3. The receiver “expects” to receive the signal ρ_(ω), however,        the signal received is λ. The signal λ is de-noised using soft        thresholding to yield the signal κ.    -   4. The “novelty signal” or “difference signal” δ=ρ_(ω)−κ carries        information about the “unexpected” distortion produced by Ton        σ_(ω).    -   5. At the receiver a lifting method is used to analyze the        novelty signal, and thereby derive the analysis coefficients of        the novelty signal.    -   6. From the novelty coefficients the inverse filter is computed        by the receiver and sent to the transmitter.    -   7. The transmitter computes an updated filter bank to encode the        message. The updated filter bank accounts for the unexpected        distortion in the channel in addition to encoding the message.    -   8. Processing continues according to 2., above. The process may        continue until the novelty signal is reduced to an acceptable        level or until a certain predefined number of iterations occur.        A Second Aspect

With respect to FIG. 6 the adaptive lifting method for optimal basesignal constriction may comprise:

-   -   1. A wavelet, ω, is selected and a message, σ is used to encode        the wavelet to form a base-band signal σ_(ω).    -   2. The base-band signal is either sent over a transmission        system T or is used to modulate a carrier ζ associated with T.    -   3. The receiver “expects” to receive the signal ρ_(ω), however,        the signal received is λ. The signal λ is de-noised using soft        thresholding to yield the signal κ.    -   4. The “novelty signal” or “difference signal” δ=ρ_(ω)−κ is        computed.    -   5. At the receiver a lifting method is used to analyze the        novelty signal, and thereby derive the analysis coefficients of        the novelty signal.    -   6. The coefficients of the novelty signal are used to update the        message.    -   7. The transmitter encodes the wavelet with the updated message.        The updated message accounts for the unexpected distortion in        the channel.    -   8. Processing continues according to 2., above. The process may        continue until the novelty signal is reduced to an acceptable        level or until a certain predefined number of iterations occur.

Having described two aspects of the invention, it will be appreciatedthat these aspects can be modified in arrangement and detail withoutdeparting from these principles. It should be understood that thecomputer programs, processes, equipment used, or methods describedherein are not related or limited to any particular type of computingenvironment, unless indicated otherwise. Various types of generalpurpose or special computing environments may be used with or performoperations in accordance with the teachings described herein. Elementsof the illustrative embodiments described as software may be implementedin hardware and vice versa.

In view of the many possible embodiments to which the principles of ourinvention may be applied, I claim as my invention such embodiments asmay come within the scope and spirit of the following claims andequivalents thereto.

1. A method for correcting a channel distortion of a known signal sentby a transmitter and received by a receiver, the method comprising thesteps of: (a) decomposing a message sent by the transmitter with atransmitter filter bank, the decomposition comprising transmitter filtercoefficients; (b) computing a novelty signal from a difference between atransmitted signal and a received signal; (c) decomposing the noveltysignal by the receiver with a receiver filter bank, the decompositioncomprising receiver filter coefficients; and (d) computing an inversereceiver filter coefficients that represent the novelty signal; whereinthe channel distortion is corrected by the inverse receiver filtercoefficients.
 2. The method according to claim 1 wherein the transmitterfilter bank utilizes wavelet lifting.
 3. The method according to claim 1wherein the receiver filter bank utilizes wavelet lifting.
 4. The methodaccording to claim 1 wherein the transmitter filter bank and thereceiver filter bank are identical.
 5. A method for inverting distortionprocesses in a telecommunication channel, the method comprising thesteps of: (a) constructing a signal from a message in a transmitterusing a first wavelet filter bank; (b) sending the signal to a receiver,wherein the signal is known to the receiver; (c) comparing in thereceiver the signal with an expected signal to form a novelty signal;(d) if the novelty signal is greater than a predetermined signal level,using by the receiver a second wavelet filter bank that is known to thetransmitter to compute coefficients that are required to represent thenovelty signal in terms of the second wavelet filter bank; (e) computingcoefficients of an inverse wavelet filter bank to the second waveletfilter bank; (f) updating by the transmitter the first wavelet filterbank using the coefficients of the inverse wavelet filter bank; (g)constructing by the transmitter an updated signal using the updatedfirst wavelet filter bank; and (h) sending the updated signal to thereceiver.
 6. The method according to claim 5 further comprising the stepof: processing the updated signal by repeating steps (c) through (h). 7.The method according to claim 5 wherein the first wavelet filter bankutilizes wavelet lifting.
 8. The method according to claim 5 wherein thesecond wavelet filter bank utilizes wavelet lifting.
 9. The methodaccording to claim 5 wherein the expected signal is known to thereceiver and has been distorted by the telecommunication channel in amanner expected by the receiver.
 10. The method according to claim 5wherein step (e) further comprises the step of: computing coefficientsof a synthesis wavelet filter bank that is related to the second waveletfilter bank, wherein the synthesis wavelet filter bank is the inversewavelet filter bank to the second wavelet filter bank.
 11. The methodaccording to claim 5 further comprising the step of: selecting by thereceiver an analysis wavelet filter bank that is amenable to analyzingthe novelty signal.
 12. The method according to claim 5 wherein thefirst wavelet filter bank and the second wavelet filter bank areidentical.
 13. The method according to claim 5 wherein said step (a)further comprises the step of: constructing the signal as a base-bandsignal that is sent directly over the telecommunication channel.
 14. Themethod according to claim 5 wherein said step (a) further comprises thestep of: constructing the signal as a base-band signal that is used tomodulate a carrier associated with the telecommunication channel. 15.The method according to claim 5 wherein said comparing step (c) furthercomprises the steps of: de-noising the signal received in the receiverusing soft thresholding to yield a second signal; and computing thenovelty signal by subtracting the second signal from the expectedsignal.
 16. A method for inverting distortion processes in atelecommunication channel, the method comprising the steps of: (a)constructing a signal from a message in a transmitter using a firstwavelet filter bank; (b) sending the signal to a receiver, wherein thesignal is known to the receiver; (c) comparing in the receiver thesignal with an expected signal to form a novelty signal; (d) if thenovelty signal is greater than a predetermined signal level, using bythe receiver a second wavelet filter bank that is known to thetransmitter to compute coefficients that are required to represent thenovelty signal in terms of the second wavelet filter bank; (e) computingcoefficients of an inverse wavelet filter bank to the second waveletfilter bank; (f) computing by the transmitter an updated messageutilizing the first wavelet filter bank and the coefficients of theinverse wavelet filter bank; (g) constructing by the transmitter anupdated signal using the updated message and the first wavelet filterbank; and (h) sending the updated signal to the receiver.
 17. The methodaccording to claim 16 further comprising the step of: processing theupdated signal by repeating steps (c) through (h).
 18. The methodaccording to claim 16 wherein the first wavelet filter bank utilizeswavelet lifting.
 19. The method according to claim 16 wherein the secondwavelet filter bank utilizes wavelet lifting.
 20. The method accordingto claim 16 wherein the expected signal is known to the receiver and hasbeen distorted by the telecommunication channel in a manner expected bythe receiver.
 21. The method according to claim 16 wherein step (f)further comprises the step of: computing coefficients of a synthesiswavelet filter bank that is related to the second wavelet filter bank,wherein the synthesis wavelet filter bank is the inverse wavelet filterbank to the second wavelet filter bank.
 22. The method according toclaim 16 further comprising the step of: selecting by the receiver ananalysis wavelet filter bank that is amenable to analyzing the noveltysignal.
 23. The method according to claim 16 wherein the first waveletfilter bank and the second wavelet filter bank are identical.
 24. Themethod according to claim 16 wherein said step (a) further comprises thestep of: constructing the signal as a base-band signal that is sentdirectly over the telecommunication channel.
 25. The method according toclaim 16 wherein said step (a) further comprises the step of:constructing the signal as a base-band signal that is used to modulate acarrier associated with the telecommunication channel.
 26. The methodaccording to claim 16 wherein said comparing step (c) further comprisesthe steps of: de-noising the signal received in the receiver using softthresholding to yield a second signal; and computing the novelty signalby subtracting the second signal from the expected signal.